Problem: Out of 1200 people polled, $30\%$ do not like radio, and $10\%$ of the people who do not like radio also do not like music.  How many people polled do not like both radio and music?
Answer: The number of people who dislike radio is $.3(1200)=360$.  Out of these, the number who also dislike music is $.1(360)=36$ people. So, $\boxed{36}$ people do not like both radio and music.